In actual practice, animals to be milked may be annoyed by the connection and disconnection of the teat cups, particularly when such connection and disconnection is effected automatically. When a teat cup is being connected, air is drawn in through the teat cup by applying a vacuum in for example a milk jar, into which the milk line runs from the teat cup, while a pulsating vacuum is often at the same time applied to the pulsation space by means of a pulsator. The liner of the teat cup then alternates between being unloaded or drawn by suction against the wall of the teat cup, and being pushed away therefrom. When the teat cup is being connected in the latter situation, the teat entering the teat cup is impeded. Such a situation also occurs when disconnection takes place at a time when the liner is pressed against the teat.